To determine if an infinite series is convergent or divergent, there are a variety of "tests" we can use. The first of these is the Divergence Test, also known as the n-th Term Test. Be careful to use this test properly. If the limit of the sequence of terms in the series is not zero, then the series is divergent. But if the limit of the sequence of terms is zero, the test is inconclusive and we have to find a different method of determining if the series is convergent or divergent.

Objectives

By the end of this topic you should know and be prepared to be tested on:

11.4.1 Use the n-th Term Test to determine if a series is divergent

11.4.2 Understand the limitations of the n-th Term Test, in particular when it is inconclusive